Question

How many solutions does the following system have:
4x + 8y = 16
3x + 6y = 9
Explain how to determine the number of solutions without solving the system. Then apply elimination, and interpret the resulting expression.

Answer 1

x=2n
y=2-n

Answer 2

you can use matrices?

Answer 3

to find x and y

Answer 4

elimination

Answer 5

4x + 8y = 16
3x + 6y = 9
givees

x + 2y = 4
x + 2y = 3

Answer 6

4x + 8y = 16 => x+2y=4
3x + 6y = 9 => x+2y =3
they contradict to each other...

Answer 7

3x + 6y = 9=y=3/2-x/2
x=2n+1
y=1-n
y=3-x/2

Answer 8

I'd say put them both into slope intercept form and examine the slopes. If the slopes are different, there is only one solution. If the slopes are the same, examine the vertical intercepts. If the intercepts are the same it has infinitely many solutions, if the intercepts are different it has no solutions.

Answer 9

Without having too much imagination, let the first equation be (1) and the second one (2). Modify the forms in the following way: Let (1)* be (1) divided by four. Let (2)* be (2) divided by three. Combine by subtraction, so (1)*-(2)* gives 0 = 1. This contradiction tells us that the system is inconsistent, and there is no solution.

Answer 10

huh? I have no idea what your saying or what reading

Answer 11

they are // lines, and don't have intercept...

Answer 12

i meant they don't intercept with each other

Answer 13

i know that, i jut don't understand what I'm suppose to do with the equations
everyone else is showing work? but this is the only problem i need help with and dont understand

Answer 14

Do you know what slope-intercept form is?

Answer 15

m= blah blah blah?

Answer 16

Not exactly...
It's y=mx+b